Orthodontic appliances, or headgear, for applying a force to a tooth are well known. Such applicances typically comprise a spring steel wire member having an outer bow and an inner bow. The left and right activating arms of the inner bow are inserted into a user's mouth and the distal end of each is inserted into a tube affixed to a tooth. In use, each inner bow arm is adjusted so as to impart a force tending to move the tooth in a desired manner. The distal end of each inner bow arm and its tube are typically of circular cross section thus allowing rotational movement relative to one another making it difficult to achieve certain precisely controlled tooth movements, and impossible to achieve certain others.